Збережено в:
| Автор: | |
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| Формат: | Preprint |
| Опубліковано: |
2022
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| Предмети: | |
| Онлайн доступ: | https://arxiv.org/abs/2206.05021 |
| Теги: |
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Зміст:
- We study two identities involving roots of unity and determinants of Hermitian matrices which have been recently proved by using the famous eigenvector-eigenvalue identity for normal matrices. In this paper, we extend these identities to a more general form by considering the class of circulant matrices. Furthermore, we give an alternative proof of Sun's identities independent of the eigenvector-eigenvalue identity, where our strategy is built upon the similarity of an unnecessarily normal matrix to a particular matrix with integer eigenvalues, derived from the Fourier transform vectors.